# Which Gas Compression Process Requires the Most Work?

• Ghost Repeater
In summary: In the isothermal case, the total energy of the gas remains the same, but because the pressure is the same, the temperature has to drop. In the isobaric case, the pressure is kept the same, but the temperature can either stay the same or drop. Which case results in more work? The case where the temperature drops. That's because in the isothermal case, the pressure doesn't have to stay the same, so the gas can lose heat to the environment and become hotter, which means you have to do more work to compress the gas.
Ghost Repeater

## Homework Statement

This is a conceptual question.

An ideal gas is compressed to half its initial volume by means of several possible processes. Which of the following processes results in the most work done on the gas? a) isothermal b) adiabatic c) isobaric d) The work done is independent of the process.

2. Homework Equations

I'm deliberately trying to avoid using equations. I'm trying to reason it out 'physically' rather than 'algebraically' using formulas.

## The Attempt at a Solution

[/B]
As I said, I'm trying to reason this through physically, by imagining what happens to the gas molecules and their energy as the volume decreases. So far, what I have is this.

More work will be required in compressing the gas adiabatically than isothermally. The reason for this is that, as you press on the gas to reduce its volume, you increase its energy by doing work on it. In an isothermal process, this energy is not allowed to increase the gas's temperature. It will be 'sapped out' of the gas by a cold bath reservoir or something of that nature. In an adiabatic process, however, the energy you transfer to the gas by doing work on it (compressing it) has no way of leaving the container, so it stays there and makes the molecules more energetic (i.e. raises temperature), which means you have to do more work still to compress the gas down further.

Is this a correct intuition about the adiabatic versus isothermal case?

As for the adiabatic vs isobaric case, as you compress the gas, in order for the pressure to stay the same, the temperature has to drop. This means the internal energy has to drop. Whereas in the adiabatic case, the internal energy had to increase. Does this mean the adiabatic case requires more work, since the molecules have more energy with which to 'resist' the compression?

Ghost Repeater said:

## Homework Statement

This is a conceptual question.

An ideal gas is compressed to half its initial volume by means of several possible processes. Which of the following processes results in the most work done on the gas? a) isothermal b) adiabatic c) isobaric d) The work done is independent of the process.

2. Homework Equations

I'm deliberately trying to avoid using equations. I'm trying to reason it out 'physically' rather than 'algebraically' using formulas.

## The Attempt at a Solution

[/B]
As I said, I'm trying to reason this through physically, by imagining what happens to the gas molecules and their energy as the volume decreases. So far, what I have is this.

More work will be required in compressing the gas adiabatically than isothermally. The reason for this is that, as you press on the gas to reduce its volume, you increase its energy by doing work on it. In an isothermal process, this energy is not allowed to increase the gas's temperature. It will be 'sapped out' of the gas by a cold bath reservoir or something of that nature. In an adiabatic process, however, the energy you transfer to the gas by doing work on it (compressing it) has no way of leaving the container, so it stays there and makes the molecules more energetic (i.e. raises temperature), which means you have to do more work still to compress the gas down further.

Is this a correct intuition about the adiabatic versus isothermal case?

As for the adiabatic vs isobaric case, as you compress the gas, in order for the pressure to stay the same, the temperature has to drop. This means the internal energy has to drop. Whereas in the adiabatic case, the internal energy had to increase. Does this mean the adiabatic case requires more work, since the molecules have more energy with which to 'resist' the compression?
Yes and yes. Now, compare isothermal with isobaric.

## 1. What is work done compressing a gas?

Work done compressing a gas refers to the amount of energy required to decrease the volume of a gas by applying external pressure. It is a measure of the change in potential energy of the gas molecules as they are pushed closer together.

## 2. How is work done compressing a gas calculated?

The work done compressing a gas can be calculated by multiplying the external pressure applied to the gas by the change in volume of the gas. This is represented by the equation W = PΔV, where W is work, P is pressure, and ΔV is the change in volume.

## 3. What factors affect the work done compressing a gas?

The work done compressing a gas is affected by the initial and final volume of the gas, the external pressure applied, and the properties of the gas itself, such as its temperature and composition.

## 4. How does work done compressing a gas relate to the laws of thermodynamics?

Work done compressing a gas is related to the first law of thermodynamics, which states that energy cannot be created or destroyed but only transferred or converted. In this case, the work done on the gas is converted into an increase in the internal energy of the gas.

## 5. Why is work done compressing a gas important?

Work done compressing a gas is important in various industrial and scientific applications, such as in refrigeration and air conditioning systems, gas storage and transportation, and in the study of thermodynamics and fluid mechanics. It also plays a role in understanding and predicting the behavior of gases in different environments.

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